Simplify the following expression: $ p = \dfrac{-1}{4} - \dfrac{q - 1}{-q - 10} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-q - 10}{-q - 10}$ $ \dfrac{-1}{4} \times \dfrac{-q - 10}{-q - 10} = \dfrac{q + 10}{-4q - 40} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{q - 1}{-q - 10} \times \dfrac{4}{4} = \dfrac{4q - 4}{-4q - 40} $ Therefore $ p = \dfrac{q + 10}{-4q - 40} - \dfrac{4q - 4}{-4q - 40} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{q + 10 - (4q - 4) }{-4q - 40} $ Distribute the negative sign: $p = \dfrac{q + 10 - 4q + 4}{-4q - 40}$ $p = \dfrac{-3q + 14}{-4q - 40}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{3q - 14}{4q + 40}$